Analysis of a stochastic ratio-dependent one-predator and two-mutualistic-preys model with Markovian switching and Holling type III functional response

作者：He, Rensheng; Xiong, Zuoliang^*; Hong, Desheng; Yin, Hongwei

来源：Advances in Difference Equations, 2016, 2016(1): 285.

DOI：10.1186/s13662-016-1011-3

• stochastic permanence
• extinction
• Markovian switching
• predator-prey model
• mutualism

In this paper, we propose a stochastic ratio-dependent one-predator and two-mutualistic-preys model perturbed by white and telegraph noise. By the M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established. These conditions are all dependent on the parameters of subsystems and the stationary probability distribution of the Markov chain. We also obtain the boundary of limit superior and inferior of the average in time of the solution under stochastic permanence. Finally, we give two examples and numerical simulations to illustrate main results.

• 出版日期2016-11-4
• 单位南昌大学